2 Answers
2

Twinking

"Twinking" is the general term for giving items to lower-level characters who can make better use of them. Many will be usable by any character you create, but occasionally, there will be some items (class-specific ones, in particular) that won't be useful to any of your characters if you've got a high-level character of that class. If that happens, just give it to a friend or sell it off in the Auction House - there isn't much point to keeping those, except for...

LLD (Low-Level Dueling)

In Diablo II, PVPers came up with a concept called Low-Level Dueling. They'd set a max level limit for the characters, which also limited the power level of items you were dealing with. If/when PVP is added to the game, LLD may become popular again. If that happens, there may be some low-level items that become particularly valuable, just for the fact that they are very powerful for their level requirement.

The only reason to keep them, next to selling them on the AH or giving them to friends is when you restart with a new character.

There are achievements for leveling 2 characters of the same class to level 60(for every class), so it may be worth doing if you're an achievement hunter and have a lot of time.

Also many items are usable for more than one class. Most armor items and all(?) rings and amulets are the same for all classes and just look differently, and a Wizzard can equip a sword, just like a barbarian or a Witch Doctor could.